Mathematical Foundations of Parity Logic

  • Michael Zaus
Part of the Studies in Fuzziness and Soft Computing book series (STUDFUZZ, volume 27)


This chapter provides a compact survey of the binary space B n and related concepts, in particular the eXclusive-OR operation xy and its generalization to the binary scalar integral ⊕ i n =1 x i and the binary vector integral ⊕ i n =1 x i for vectors xB n . We present these mathematical foundations in standard computer science nomenclature, but we will refer also to the nomenclature of APL, because the binary vector integral in section 2.3 has its origin in APL ([IVE62], [IVE78], [LAN93], [LOC89], [ZA95]).


Binary Vector Parity Logic Mathematical Foundation Symmetry Operator Boolean Ring 


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Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Michael Zaus
    • 1
  1. 1.Institute for Cognitive ScienceUniversity of OldenburgOldenburgGermany

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